This Brief describes a method of machining and assembly when the depth of corrugations far exceeds the width and conventional machining is not practical. The horn is divided into easily machined, individual rings with shoulders to control the depth. In this specific instance, each of the corrugations is identical in profile, and only differs in diameter and outer profile. The horn is segmented into rings that are cut with an interference fit (zero clearance with all machining errors biased toward contact). The interference faces can be cut with a reverse taper to increase the holding strength of the joint. The taper is a compromise between the interference fit and the clearance of the two faces during assembly. Each internal ring is dipped in liquid nitrogen, then nested in the previous, larger ring. The ring is rotated in the nest until the temperature of the two parts equalizes and the pieces lock together. The resulting assay is stable, strong, and has an internal finish that cannot be achieved through other methods.